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| Titre: | Systems having liouvillian first integrals and Non-Algebraic limit cycles |
| Auteur(s): | Grazem, Mohamed
Bendjeddou, Ahmed
Cheurfa, Rachid |
| Mots-clés: | Limit Cycles
Non-Algebraic
First Integrals
Systems Having Liouvillian |
| Date de publication: | 2021 |
| Editeur: | Tsing Hua University |
| Collection/Numéro: | Applied Mathematics E - Notes/ Vol.21 (2021);pp. 119-128 |
| Résumé: | We consider the class of polynomial differential equations ẋ = Pm (x, y)+Pm+n (x, y), ẏ = Qm (x, y)+ Qm+n (x, y) for m, n ≥ 1 and where Pi and Qi are homogeneous polynomials of degree i. Inside this class, we identify a new subclass of Liouvillian integrable systems, under suitable conditions such Liouvillian integrable systems can have at most one limit cycle, and when it exists, is non-algebraic and hyperbolic. Then we study the general systems of the systems studied in [9], which allow us to find the necessary and suffi cient conditions for the existence and non-existence of limit cycles |
| URI/URL: | http://dlibrary.univ-boumerdes.dz:8080/handle/123456789/7545 |
| ISSN: | 1607-2510 |
| Collection(s) : | Publications Internationales
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